where the penalty coefficient \(\theta \)  is a function of the target tolerance \(\epsilon > 0\)  for satisfying the linear coupling constraints.
In [1]}, this idea is exploited to design algorithms that globally converge to \(\epsilon \) -stationary points of (REF ) in \(O(\epsilon ^{-6})\)  iterations.
Moreover, the algorithms require the global solution of NLP problems [1]}, which can be numerically demanding when the local subproblems are nonconvex.
A similar quadratic penalty idea is adopted in [3]} although it requires the augmented Lagrangian function (with respect to all nonlinear and coupling constraints) to satisfy the Kurdyka-Łojasiewicz property [4]}; furthermore, that analysis does not reconcile the penalty formulation (REF ) with the original formulation (REF ).
Each iteration linearizes the augmented Lagrangian function around the previous iterate that is then alternately minimized with respect to the \(T\)  blocks.
Other approaches using local linear and convex approximations of the nonlinear constraints or of the augmented Lagrangian function, and methods establishing convergence under additional assumptions such as coercivity of the objective function, have been proposed in [5]}, [6]}, [7]}, [8]}.
